The basic answer is: when a man and woman married, the law considered the wife’s legal identity to be absorbed into her husband’s, this meant that everything a woman owned before her marriage became the property of her husband, to dispose of as he pleased. This did not change until the Married Women’s Property Act of 1882 that married women were given the same property rights as single women.
Marriage settlements, which were essentially prenuptual agreements, were the means that parents and guardians used to circumvent this problem. The settlement would set up a separate trust for the wife and guarentee her access to certain amounts of funds during her husband’s life and after his death. Exact terms would be negotiated and contracted out by the parties involved and could include other provisions as well. This way a father could prevent a profligate son-in-law from spending all his money and leaving his daughter destitute.
All of this provided fortune hunters like George Wickham with ample reason to want to elope with an heiress. The heiress already owns her money or property, so there is no threat that her father will decide to give her nothing, or provide her with some other nonmonetary form of support following the marriage and by eloping he has prevented the formation of a marriage settlement which would limit his access to his wife’s money.